Book contents
- Frontmatter
- Dedication
- Contents
- List of Figures
- List of Tables
- Acknowledgements
- Nomenclature
- 1 Introduction
- 2 The Boltzmann Equation 1: Fundamentals
- 3 The Boltzmann Equation 2: Fluid Dynamics
- 4 Transport in Dilute Gas Mixtures
- 5 The Dilute Lorentz Gas
- 6 Basic Tools of Nonequilibrium Statistical Mechanics
- 7 Enskog Theory: Dense Hard-Sphere Systems
- 8 The Boltzmann–Langevin Equation
- 9 Granular Gases
- 10 Quantum Gases
- 11 Cluster Expansions
- 12 Divergences, Resummations, and Logarithms
- 13 Long-Time Tails
- 14 Transport in Nonequilibrium Steady States
- 15 What’s Next
- Bibliography
- Index
13 - Long-Time Tails
Published online by Cambridge University Press: 18 June 2021
- Frontmatter
- Dedication
- Contents
- List of Figures
- List of Tables
- Acknowledgements
- Nomenclature
- 1 Introduction
- 2 The Boltzmann Equation 1: Fundamentals
- 3 The Boltzmann Equation 2: Fluid Dynamics
- 4 Transport in Dilute Gas Mixtures
- 5 The Dilute Lorentz Gas
- 6 Basic Tools of Nonequilibrium Statistical Mechanics
- 7 Enskog Theory: Dense Hard-Sphere Systems
- 8 The Boltzmann–Langevin Equation
- 9 Granular Gases
- 10 Quantum Gases
- 11 Cluster Expansions
- 12 Divergences, Resummations, and Logarithms
- 13 Long-Time Tails
- 14 Transport in Nonequilibrium Steady States
- 15 What’s Next
- Bibliography
- Index
Summary
Time correlation functions appearing in the Green-Kubo expressions for transport coefficients are studied by using kinetic theory. Of particular interest is the theory for the algebraic, t??d=2 long time time decays, or long time tails, first seen in computer simulations of the velocity autocorrelation function for tagged particle diffusion. Kinetic equations for distribution functions that determine time correlation functions are obtained using cluster expansions, and divergences appear due to the effects of correlated sequences of binary collisions. The ring resummation introduced in Chapter 12 leads to mode-coupling expressions containing products of two hydrodynamic mode eigenfunctions. The sum of these contributions leads directly to the long time tails, quantitatively in agreement with computer simulations. Mode coupling theory also leads to an explanation of the observed, intermediate time, molasses tails, and to the existence of fractional powers in sound dispersion relations, for which there is strong experimental evidence.
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- Information
- Contemporary Kinetic Theory of Matter , pp. 507 - 540Publisher: Cambridge University PressPrint publication year: 2021